So, first I'd like to thank you all for working so hard helping me figure this out.
I have good and bad news today, ultimately good news overall though.
So I went into shop today and took all your suggestions and combined them and sure enough, it was turning true again. First, I re-cut my center at 60 degrees. Then, I lubed the dead center and live center. I put my piece in and tightened it, not too hard this time, just enough. Turned on the lathe and to my amazement the piece was turning perfectly true and not wobbling. Step 1, done.
Step 2, check for tailstock runout. It was .004 out so I adjusted the tailstock and got it within .001 difference, so that was a win.
Step 3, which should have been set my tool height, didn't go so well. I was running my 60 degree thread cutting tool a bit too high the entire time in shop today and couldn't figure out why my piece was just hitting the end and bumping back in. One time, it caught the end and jammed the tool bit into the piece so I had to stop the machine. I had to find my threads again with the help of others. So I kept cutting passes of about .010-0.015 per pass. Eventually right before break, my machine jammed again. Then I told a co-student about the problem and he asked if my tool height was right. I said, wow I forgot to set it..
So I come back from break, set my tool height correctly and sure enough the threads were cutting much nicer. The biggest issue here was, I couldn't re-find my threads correctly. I used the compound in-feed to just scrape the right side of the thread, etc...then.... I noticed that the thread cutting tool was only cutting threads on the left side of my external threads. I should have stopped it there, but I kept going. Eventually I got to the end of the thread, like 60 passes later, got to my tolerance and saw there was a small lip to the left of my threads. Sure enough the nut didn't thread on and my piece was ruined so I have to start over because it's a 100% or 0 project.
So in all, it was quite the learning experience. The next time I am going to set my tool height and take everything I've learned today to heart. But I thank you guys again for your help and I very much appreciate it. I'll be sticking around on this forum for a while. I'll keep you guys posted and eventually get some more pics and stuff to share. My instructor has helped me throughout these issues and I'm just learning through each mistake. Hopefully I've learned all I need to so far for this project because it's been a LOT.